Gary-
Most slash chords are hard to play on an ukulele, especially with reentrant tuning..... they're really for guitar or piano, instruments with more range. Like JJ said, the chord is really just the the note in front of the slash. The note after the slash tells you what note to play as the lowest note in the voicing.
An F major chord is composed of the notes F, A, and C. When you play F/A, you play an F major chord, making sure that the 'A' is the lowest voiced note, sounding as the bass. If you have your uke strung with a low G, you are playing F/A whenever you play the standard F chord fingering (2 0 1 0). That '2' on the G string is an 'A', and with a low G, it is the lowest pitched note in that particular voicing.
The slash chords are in this arrangement because that's how Lyle plays it on the guitar - if you play these chords on the guitar, using the particular bass note for each chord voicing, you get a really nice chromatic sounding bass line that compliments the melody and fills out the guitar part - especially if you're fingerpicking. That's why most slash chords just don't work on uke, especially with a high G. The instrument doesn't have the range to accompany itself with a built in bass line. That's why this song is hard to play on uke - you can play the chords, but you don't get that nice walking bass line that really gives the tune its distinctive sound.
This is one of the reasons I keep my uke tuned low G. As a guitarist, it's what I'm used to and I like being able to use those lower voiced notes as much as possible.
Slash chords do serve a purpose for the uke, though, especially if you're playing with others - they let you know what's going on harmonically with the tune, even if it's not something you are playing on your instrument. Also, some slash chords are used to represent more complex chords in a quick easy to read symbol. If you see C/D in a jazz tune, it's probably a Dsus chord.....